Re: [math-fun] mis-defining limits

On 9/12/06, Eugene Salamin <gene_salamin@yahoo.com> wrote:

Plot g(1-exp(-x)). For x > 6, the graph becomes periodic.

g(x) ~ 0.5 + 0.027 sin(2 pi (x - 0.526) /1.385).

Gene

I think maybe the above should have read g(1-exp(-x)) = 0.5 + 0.027 sin(2 pi (x - 0.526) /1.385) which does look to be true as x -> 1- with error O(1-x). All that spiel about g(x) converging on the unit circle is codswallop, because the relation g(x) + g(x^2) = x fails to hold in the limit --- nice one! If I'd listened to advice and "used a calulator" in the first place, I might have spared myself a very red face here. WFL